As in [1]}, the offsets \((\Delta x,\Delta y)\)  are modeled as a mixture of \(M\)  bivariate normal distributions with the parameters for each of the distribution \(i\)  to be \((\mu _{x,i},\mu _{y,i},\sigma _{x,i},\sigma _{y,i},\rho _{xy,i})\) . There is an additional vector \(\Pi \)  of length \(M\)  which consists of the mixing weights for the Gaussian Mixture Model (GMM). Therefore, at each time-step \(t\) , hidden state of \(\tilde{G}\)  is mapped to a vector \(\tilde{y}\)  of size \(6M\) , from where the parameters of the GMM are sampled. The distribution of the offsets are given as:
\(p(\Delta x,\Delta y) = {\sum _{j=1}^M \Pi _j \mathcal {N}(\Delta x,\Delta y \mid \mu _{x,j},\mu _{y,j},\sigma _{x,j},\sigma _{y,j},\rho _{xy,j})}, \quad \text{where} \quad \sum _{j=1}^M \Pi _j = 1\) 
